Model identification of a noncausal 2-D AR process using a causal 2-D AR model on the nonsymmetric half-plane

If a noncausal two-dimensional (2-D) autoregressive (AR) process is bi-causal, there exists a causal 2-D AR process on the nonsymmetric half-plane having the same autocorrelations as the noncausal 2-D AR process. A formula is presented to relate the AR coefficients of the noncausal 2-D AR process with those of the causal 2-D AR process on the nonsymmetric half plane. The 2-D Yule-Walker equations are derived for causal 2-D AR models on the nonsymmetric half plane. A computationally efficient order-recursive algorithm is proposed to solve the 2-D Yule-Walker equations. Using the autocorrelation equivalence relation and the order-recursive algorithm, we can easily identify a noncausal 2-D AR process from its autocorrelations.     

Two-dimensional spectrum estimation using noncausal autoregressive models

Two-dimensional (2-D) spectrum estimation from raw data is of interest in signal and image processing. A parametric technique for spectrum estimation using 2-D noncausal autoregressive (NCAR) models is given. The NCAR models characterize the statistical dependency of the observation at location s on its neighbors in all directions. This modeling assumption reduces the spectrum estimation problem to two subproblems: the choice of appropriate structure of the NCAR model and the estimation of parameters in NCAR models. By assuming that the true structure of the NCAR model is known, we first analyze the existence and uniqueness of Gaussian maximum likelihood (GML) estimates of NCAR model parameters. Due to the noncausal nature of the models, the computation of GML estimates is burdensome. By assuming specific boundary conditions, computationally tractable expressions are obtained for the likelihood function. Expressions for the asymptotic covariance matrix of the GML estimates as well as the simultaneous confidence bands for the estimated spectrum using GML estimates are derived. Finally, the usefulness of the method is illustrated by computer simulation results.     

Model Specification of a Noncausal 3-D AR Process Using a Causal 3-D AR Model on the Nonsymmetric Half-Space

There exists a causal 3-D AR process on the nonsymmetric half-space having the same autocorrelations as a noncausal 3-D AR process. A formula is presented to relate the AR coefficients of the noncausal 3-D AR process with those of the causal 3-D AR process on the nonsymmetric half-space. The 3-D Yule-Walker equations are derived for causal 3-D AR models on the nonsymmetric half-space, and a computationally efficient order-recursive algorithm is proposed to solve the 3-D Yule-Walker equations. We can easily specify a noncausal 3-D AR process from its autocorrelations using the autocorrelation equivalence relation, the formula of the AR coefficients and the order-recursive algorithm.     

High resolution two-dimensional minimum free energy AR spectral estimation

We extend the minimum free energy (MFE) parameter estimation method to 2-D fields. This 2-D MFE method may be used to determine autoregressive (AR) model parameters for spectral estimation of 2-D fields. It may also be used to provide AR models for texture synthesis. The performance of the technique for closely spaced sinusoids in white noise is demonstrated by numerical example. Better results can be achieved than with the multidimensional Levinson algorithm.     

Multiscale representations of Markov random fields

Recently, a framework for multiscale stochastic modeling was introduced based on coarse-to-fine scale-recursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. The authors show that this model class is also quite rich. In particular, they describe how 1-D Markov processes and 2-D Markov random fields (MRFs) can be represented within this framework. The recursive structure of 1-D Markov processes makes them simple to analyze, and generally leads to computationally efficient algorithms for statistical inference. On the other hand, 2-D MRFs are well known to be very difficult to analyze due to their noncausal structure, and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification. In contrast, their multiscale representations are based on scale-recursive models and thus lead naturally to scale-recursive algorithms, which can be substantially more efficient computationally than those associated with MRF models. In 1-D, the multiscale representation is a generalization of the midpoint deflection construction of Brownian motion. The representation of 2-D MRFs is based on a further generalization to a “midline” deflection construction. The exact representations of 2-D MRFs are used to motivate a class of multiscale approximate MRF models based on one-dimensional wavelet transforms. They demonstrate the use of these latter models in the context of texture representation and, in particular, they show how they can be used as approximations for or alternatives to well-known MRF texture models     

空间域的马尔可夫立体网状结构模型及其应用

本文提出三维马尔可夫随机变量的网状结构模型,探讨三维图象的建模及其图象描述的应用。对所述空间域的马尔可夫立体网状结构模型进行了详细的理论证明。为三维图象的描述、建模、分割、分类等提供了一个较有力的工具。最后,用实例给出一种三维图象的建摸及其图象描述。     

Two-dimensional affine generalized fractional Fourier transform

As the one-dimensional (1-D) Fourier transform can be extended into the 1-D fractional Fourier transform (FRFT), we can also generalize the two-dimensional (2-D) Fourier transform. Sahin et al. (see Appl. Opt., vol.37, no. 11, p.2130-41, 1998) have generalized the 2-D Fourier transform into the 2-D separable FRFT (which replaces each variable 1-D Fourier transform by the 1-D FRFT, respectively) and the 2-D separable canonical transform (further replaces FRFT by the canonical transform). Sahin et al., (see Appl. Opt., vol.31, no.23, p.5444-53, 1998), have also generalized it into the 2-D unseparable FRFT with four parameters. In this paper, we introduce the 1-D affine generalized fractional Fourier transform (AGFFT). It has even further extended the 2-D transforms described above. It is unseparable, and has, in total, ten degrees of freedom. We show that the 2-D AGFFT has many wonderful properties, such as the relations with the Wigner distribution, shifting-modulation operation, and the differentiation-multiplication operation. Although the 2-D AGFFT form seems very complex, in fact, the complexity of the implementation will not be more than the implementation of the 2-D separable FRFT. Besides, we also show that the 2-D AGFFT extends many of the applications for the 1-D FRFT, such as the filter design, optical system analysis, image processing, and pattern recognition and will be a very useful tool for 2-D signal processing     

Fitting MA models to linear non-Gaussian random fields using higherorder cumulants

A general (possibly nonminimum phase and/or asymmetric noncausal) two-dimensional (2-D) moving average (MA) model driven by a zero-mean i.i.d. 2-D sequence is considered. The input sequence is not observed. The signal observations may be noisy. We consider the problems of model order determination and model parameter estimation using the higher order (third- or fourth-order, for example) cumulants of the 2-D signal. Second-order statistics of the data can consistently identify only a smaller class of MA models. The proposed approaches are illustrated via computer simulations     

An alternating direction algorithm for total variation reconstruction of distributed parameters

Augmented Lagrangian variational formulations and alternating optimization have been adopted to solve distributed parameter estimation problems. The alternating direction method of multipliers (ADMM) is one of such formulations/optimization methods. Very recently, the number of applications of the ADMM, or variants of it, to solve inverse problems in image and signal processing has increased at an exponential rate. The reason for this interest is that ADMM decomposes a difficult optimization problem into a sequence of much simpler problems. In this paper, we use the ADMM to reconstruct piecewise-smooth distributed parameters of elliptical partial differential equations from noisy and linear (blurred) observations of the underlying field. The distributed parameters are estimated by solving an inverse problem with total variation (TV) regularization. The proposed instance of the ADMM solves, in each iteration, an l(2) and a decoupled l(2) - l(1) optimization problems. An operator splitting is used to simplify the treatment of the TV regularizer, avoiding its smooth approximation and yielding a simple yet effective ADMM reconstruction method compared with previously proposed approaches. The competitiveness of the proposed method, with respect to the state-of-the-art, is illustrated in simulated 1-D and 2-D elliptical equation problems, which are representative of many real applications.     

一种基于激光测距技术的三维可视化系统

构建一个基于激光距离探测器的物体表面三维建模与成像系统,通过对运动物体的多次连续扫描,根据采集到的二维距离信息和扫描仪的运动方程以及转动姿态,建立物体表面的三维空间模型.其作为一个PC/104嵌入式系统,可应用于室内物体表面建模,也适用于将扫描仪挂载在车辆或小型无人机等移动平台上,进行室外地表环境的三维可视化.     

Parallel image processing with the block data parallel architecture

Many digital signal and image processing algorithms can be speeded up by executing them in parallel on multiple processors. The speed of parallel execution is limited by the need for communication and synchronization between processors. In this paper, we present a paradigm for parallel processing that we call the block data flow paradigm (BDFP). The goal of this paradigm is to reduce interprocessor communication and relax the synchronization requirements for such applications. We present the block data parallel architecture which implements this paradigm, and we present methods for mapping algorithms onto this architecture. We illustrate this methodology for several applications including two-dimensional (2-D) digital filters, the 2-D discrete cosine transform, QR decomposition of a matrix and Cholesky factorization of a matrix. We analyze the resulting system performance for these applications with regard to speedup and efficiency as the number of processors increases. Our results demonstrate that the block data parallel architecture is a flexible, high-performance solution for numerous digital signal and image processing algorithms     

Bispectral analysis and model validation of texture images

Statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian and/or asymmetric. In this paper, higher than second-order statistics are used to derive and implement 2-D Gaussianity, linearity, and spatial reversibility tests that validate the respective modeling assumptions. The nonredundant region of the 2-D bispectrum is correctly defined and proven. A consistent parameter estimator for nonminimum phase, asymmetric noncausal, 2-D ARMA models is derived by minimizing a quadratic error polyspectrum matching criterion. Simulations on synthetic data are performed and the results of the bispectral analysis on real textures are reported.     

Design of 3-D Noncausal Filters with Small Roundoff Noise and No Overflow Oscillations

The contribution of this paper consists of two individual parts. First, an invertible mapping technique is presented for 3-D digital system design, and it is applied to approximate 3-D noncausal filters in the spatial domain. Secondly, an algorithm is proposed for obtaining a structure for 3-D IIR filters with small roundoff noise and no overflow oscillations. The design of noncausal filters can be carried out by three steps: 1), a given noncausal impulse response is transformed into the first octant using the proposed 3-D invertible mapping technique; 2), the transformed impulse response in the first octant is approximated by balanced model reduction of 3-D separable denominator systems;3), the resultant 3-D IIR filter is transformed back to the original coordinates.     

Automatic 3D modeling of textured cultural heritage objects

A widespread use of three-dimensional (3-D) models in cultural heritage application requires low cost equipment and technically simple modeling procedures. In this context, methods for automatic 3-D modeling of textured objects will play a central role. Such methods need fully automatic techniques for 3-D views registration and for the removal of texture artifacts. This paper proposes a contribution in this direction based on image processing approaches. The proposed procedure is very robust and simple. It does not require special equipment or skill in order to make textured 3-D models. The results of this paper, originally conceived to address the costs issues of cultural heritage modeling, can be profitably exploited also in other modeling applications.     

多尺度系统理论研究概况

在许多应用领域中,通常要对出现在不同尺度的现象进行分析和辨识,最近引入的多尺度框架使这一分析成为可能。该文简单介绍了多尺度系统理论的发展概况以及多尺度框架在估计和数据融合中的应用,分析了多尺度模型、平滑误差模型以及两类多尺度实现模型,并指出了目前急需解决的问题。     

Maximum likelihood estimation of signals in autoregressive noise

Time series modeling as the sum of a deterministic signal and an autoregressive (AR) process is studied. Maximum likelihood estimation of the signal amplitudes and AR parameters is seen to result in a nonlinear estimation problem. However, it is shown that for a given class of signals, the use of a parameter transformation can reduce the problem to a linear least squares one. For unknown signal parameters, in addition to the signal amplitudes, the maximization can be reduced to one over the additional signal parameters. The general class of signals for which such parameter transformations are applicable, thereby reducing estimator complexity drastically, is derived. This class includes sinusoids as well as polynomials and polynomial-times-exponential signals. The ideas are based on the theory of invariant subspaces for linear operators. The results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems. The authors briefly discuss some applications such as spectral analysis, broadband/transient detection using line array data, and fundamental frequency estimation for periodic signals     

基于因子图的自适应波束形成

图模型具有广泛的应用,它为许多问题提供了一种新的表达方式和研究思路。因子图作为一类重要的图模型,尤其适用于多变量的复杂统计模型。因子图的引入可以使复杂的多变量问题得到简化。因子图理论在系统建模以及信号检测和估计算法中有着重要的应用。国内外不少学者将因子图理论应用于复杂的通信信号处理,但目前很少见到将因子图理论应用在雷达信号处理中。为了将因子图理论作为一种有效的工具应用于雷达信号处理,提出了用因子图理论实现雷达信号处理中的自适应波束形成技术（ADBF）的方法,这为用图模型研究雷达信号处理提供了一个很好的思路。     

Image modeling using inverse filtering criteria with application totextures

Statistical approaches to image modeling have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian. This constrains the parameters of noncausal image models to be symmetric and, therefore, the underlying random field to be spatially reversible. Research indicates that this assumption may not be always valid for texture images. In this paper, higher- than second-order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving-average (ARMA) image models with known orders. Contrary to existing approaches, FIR inverse filters are employed and image models with zeros on the unit bicircle can be handled. One of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date, Consistency of these estimators is established, and their performance is evaluated with Monte Carlo simulations as well as texture classification and synthesis experiments.